Question: Solve for $x$ and $y$ by deriving an expression for $x$ from the second equation, and substituting it back into the first equation. $\begin{align*}5x-8y &= 4 \\ -5x+6y &= -8\end{align*}$
Solution: Begin by moving the $y$ -term in the second equation to the right side of the equation. $-5x = -6y-8$ Divide both sides by $-5$ to isolate $x$ $x = {\dfrac{6}{5}y + \dfrac{8}{5}}$ Substitute this expression for $x$ in the first equation. $5({\dfrac{6}{5}y + \dfrac{8}{5}}) - 8y = 4$ $6y + 8 - 8y = 4$ Simplify by combining terms, then solve for $y$ $-2y + 8 = 4$ $-2y = -4$ $y = 2$ Substitute $2$ for $y$ in the top equation. $5x-8( 2) = 4$ $5x-16 = 4$ $5x = 20$ $x = 4$ The solution is $\enspace x = 4, \enspace y = 2$.